My zimbra NE setup is quite similar to your proposed setup. Two servers on private network 10.0.0.x. The smtp & mailbox server NATd against our public IPs to handle in/out mails. Meanwhile, my ldap/backup server dont have public IPs.
As for DNS, I have set-up 2 dns (already available at the installation time at two separate boxes). Internal dns for local usage and external dns for outside usage. By having the internal dns, somehow our local mail traffic is well diverted locally without going to the outside and back to the inside.
Basically, thats it. Its been running fine.. at least for now
